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%I #5 Jan 19 2019 04:15:43
%S 735,2172,3484,6324,6747,6867,7424,7865,14012,14640,35321,39284,42172,
%T 47724,57075,60155,63664,89975,104923,105412,113283,114204,149144,
%U 151959,153924,155708,176860,189780,221705,230124,244035,250995,327700,349811,351075,357752
%N The average of prime factors of n and n+1 is the same.
%C Up to 10^13 there is only one triple of consecutive numbers, starting at 18140055498, which have the same average of prime factors.
%H Giovanni Resta, <a href="/A227755/b227755.txt">Table of n, a(n) for n = 1..1000</a>
%e 735 is in the sequence since 735 = 3*5*7^2, 736 = 2^5*23 and (3+5+7+7)/4 = (2+2+2+2+2+23)/6.
%t avepa[n_] := Block[{f = FactorInteger[n]}, Total[Times @@@ f]/Total[Last /@ f]]; Select[Range[2,10^5], avepa[#] == avepa[#+1] &]
%Y Cf. A227754.
%K nonn,easy
%O 1,1
%A _Giovanni Resta_, Jul 26 2013